Could you give a clue how to calculate the $map$, for example, $map(R^{0∣d},M)$ for any supermanifold $M$?
For $d=1$, it is well-known (and due to Kontsevich, I think), that $map(R^{0|1},M)$ is the total space of the odd tangent bundle $\Pi TM$ of $M$.
If $U$ is a superdomain of dimension $p|q$, then $map(R^{0|d},U)=U\times R^{qd|pd}$R^{pr+qs|ps+qr}$where$(r+1)|s=2^{d-1}|2^{d-1}$is the graded dimension of$\bigwedge R^d$. This you can check using the definition of$map$and the characterisation of morphisms of supermanifolds as given in Leites. Another good source on this subject (for$d=1$), is the paper "Differential forms and 0-dimensional supersymmetric field theories" by Hohnhold, Kreck, Stolz and Teichner. 1 @Ma: As an answer to your following question: Could you give a clue how to calculate the$map$, for example,$map(R^{0∣d},M)$for any supermanifold$M$? Take a look at arXiv:math/0307303, where this question is discussed. For$d=1$, it is well-known (and due to Kontsevich, I think), that$map(R^{0|1},M)$is the total space of the odd tangent bundle$\Pi TM$of$M$. If$U$is a superdomain of dimension$p|q$, then$map(R^{0|d},U)=U\times R^{qd|pd}$. This you can check using the definition of$map$and the characterisation of morphisms of supermanifolds as given in Leites. Another good source on this subject (for$d=1\$), is the paper "Differential forms and 0-dimensional supersymmetric field theories" by Hohnhold, Kreck, Stolz and Teichner.